Car will not crank over

I purchased this vehicle just over a year ago, was intermittently not starting. If I let it sit for a few minutes, it would start. I took it to be looked at but because it started at the garage they couldn't diagnose it. Then it wouldn't start at all and I had it towed back. They said it was the starter and replaced it. I had replaced the started on my previous element and didn't feel this was the same problem, but I'm not a mechanic and I needed the car back. It worked for about a week and then wouldn't start again. I was able to jump it but it wouldn't accelerate and all the dash lights came on (ABS, engine, maintenance required, oil, etc.). I had it towed back and they said the alternator and battery were bad and replaced those. The day after I got it back it broke down while I was driving at night. The gauges all dropped, the lights went dim and the car just died. I had it towed to the nearest garage and they said it needed a new computer because the current one wasn't "recognizing the replaced parts". They said the part would cost $904.57, and that it would have to be ordered and replaced and programmed by a certified Honda service station. I then had it towed to a Honda service station and they are now telling me the car doesn't have a computer, they have no idea what I'm talking about and they want to charge me $500.00 to run a full diagnostic. I cannot afford to pay $500.00 just for them to tell me what's wrong after the $1,200.00 I already put in for parts I may not have even needed, and then another $1,000.00 at least to have it fixed. Can someone tell me what part I should direct their focus to? Have others had this issue, and if so, is the car even worth fixing? I'd rather put the money toward a new car if this is going to keep happening.